Heat the oven to 160°C/gas mark 3.
Butter a 22cm round, loose-bottomed cake tin, then line the base with baking parchment.
Beat the butter and caster sugar together in a large bowl until it is light and fluffy.
Gradually pour in the beaten eggs, a little at a time, until you have added two thirds, adding flour if it curdles.
Fold in the remaining egg, followed by the ground almonds and, finally, the flour, then combine everything gently.
Add two thirds of the apple pieces to the cake mixture, followed by all the blackberries.
Turn the mixture into the prepared tin, then smooth it out evenly.
Scatter the remaining apple pieces over the surface of the cake.
Scatter the cinnamon, Demerara sugar, and butter over the top.
Bake for 50-55 minutes, or until a skewer inserted into the cake comes out clean.
Remove the cake from the oven, then scatter over the toasted hazelnuts.
When the cake is cool, dust lightly with icing sugar, then cut into slices to serve.
8 servings